has a non empty intersection with \(\mathcal {V}(0)\) . The vector is said relevant [1]} if the intersection includes a \((n-1)\) -dimensional face of \(\mathcal {V}(0)\) .
We denote by \(\tau _{f}\)  the number of relevant Voronoi vectors, referred to as the Voronoi number in the sequel.
For root lattices [1]}, the Voronoi number is equal to the kissing number \(\tau \) , defined as the number of points at a distance \(d(\Lambda )\)  from the origin.
For random lattices, we have \(\tau _{f}=2^{n+1}-2\)  (with probability 1) [3]}.
The set \(\mathcal {T}_f(x)\) , for \(x \in \Lambda \) , denotes the set of lattice points having a common Voronoi facet with \(x\) .
The theta series of \(\Lambda \)  is [1]}
\(\Theta _{\Lambda }(q)=\sum _{x \in \Lambda } q^{\Vert x\Vert ^2}=\sum _{\ell =0}^\infty \tau _\ell q^\ell ,\) 
